Clemson University TigerPrints All Dissertations Dissertations 8-2013 Essays on Service Strategies: Evidence from Banking and Healthcare Industries Sriram Venkataraman Clemson University, [email protected]Follow this and additional works at: hps://tigerprints.clemson.edu/all_dissertations Part of the Management Sciences and Quantitative Methods Commons is Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints. For more information, please contact [email protected]. Recommended Citation Venkataraman, Sriram, "Essays on Service Strategies: Evidence from Banking and Healthcare Industries" (2013). All Dissertations. 1188. hps://tigerprints.clemson.edu/all_dissertations/1188
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Clemson UniversityTigerPrints
All Dissertations Dissertations
8-2013
Essays on Service Strategies: Evidence fromBanking and Healthcare IndustriesSriram VenkataramanClemson University, [email protected]
Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations
Part of the Management Sciences and Quantitative Methods Commons
This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations byan authorized administrator of TigerPrints. For more information, please contact [email protected].
Recommended CitationVenkataraman, Sriram, "Essays on Service Strategies: Evidence from Banking and Healthcare Industries" (2013). All Dissertations.1188.https://tigerprints.clemson.edu/all_dissertations/1188
Since p is greater than 0.1, we fail to reject H0 that mean efficiency of U.S. banks
and Indian banks are equal.
Next, we test the null hypothesis H0 : µ1,θ = µ2,θ versus the alternative H1 :
µ1,θ > µ2,θ, where µ1,θ is the expected efficiency of public Indian banks and µ2,θ is the
expected efficiency of domestic private Indian banks. The number of public Indian
banks in our data is n1 = 23, and the sample size of domestic private banks in India
is n2 = 16. The sample size of subset of public and domestic private banks are
n1,κ = b23(2∗0.25)c = 4 and n2,κ = b16(2∗0.25)c = 4 respectively. The mean efficiency
estimates of public and domestic private banks are µ1,n1 = 1 and µ2,n2 = 0.989
respectively, and the mean efficiency estimates of subset of public and domestic private
banks are µ1,n1,κ = 1 and µ2,n2,κ = 0.983 respectively. The standard deviations of
efficiency estimates of public and domestic private banks in India are σ21,θ,n1
= 0 and
σ22,n2
= 0.000493 respectively. The mean efficiency estimates of two subsamples of
public banks are µ(1)1,m1,1
= 1 and µ(2)1,m1,2
= 1, and the mean efficiency estimates of two
subsamples of domestic private banks are µ(1)2,m2,1
= 0.993 and µ(2)2,m2,2
= 1. The test
statistic computed using Equation 1.31 is τn = 4.8138. Since this is a one-tailed test,
the p-value is given by
p = 1− Φ(τn1,n2) = 1− Φ(4.8138) = 0.000001. (1.34)
Since p is less than 0.01, we reject H0 that mean efficiency of public banks and do-
mestic private banks in India are equal. So, public Indian banks have significantly
26
higher expected efficiency than domestic private Indian banks even after 20 years
of liberalization. We test for stochastic dominance of true distribution of efficiency
estimates of public banks over true distribution of efficiency estimates of domestic
private banks using Kolmogorov Smirnov test. Note that rejection of H0 : µ1,θ = µ2,θ
versus the alternative H1 : µ1,θ > µ2,θ is a necessary but not sufficient condition for
stochastic dominance. We use ks.test function in R to test stochastic dominance. We
reject the null hypothesis that the true distribution function of efficiency estimates
of public banks is equal to the true distribution function of efficiency estimates of
domestic private banks with a p-value of 0.000014. This implies that the true dis-
tribution function of public banks’ efficiency estimates stochastically dominates the
true distribution function of domestic private banks’ efficiency estimates in India.
Finally, we test the null hypothesis H0 : µ1,θ = µ2,θ versus the alternative
H1 : µ1,θ > µ2,θ, where µ1,θ is the expected efficiency of public Indian banks and µ2,θ
is the expected efficiency of foreign banks operating in India. The number of public
Indian banks in our data is n1 = 23, and the number of foreign banks in India is
n2 = 24. The sample size of subset of public and foreign banks in India are n1,κ =
b23(2∗0.25)c = 4 and n2,κ = b24(2∗0.25)c = 4 respectively. The mean efficiency estimates
of public and foreign banks in India are µ1,n1 = 1 and µ2,n2 = 0.889 respectively, and
the mean efficiency estimates of subset of public and foreign banks are µ1,n1,κ = 1 and
µ2,n2,κ = 0.799 respectively. The standard deviations of efficiency estimates of public
and foreign banks in India are σ21,θ,n1
= 0 and σ22,n2
= 0.0459 respectively. Finally,
the mean efficiency estimates of the two subsamples of public banks are µ(1)1,m1,1
= 1
and µ(2)1,m1,2
= 1, and the mean efficiency estimates of the two subsamples of foreign
banks in India are µ(1)2,m2,1
= 0.996 and µ(2)2,m2,2
= 0.920. The computed test statistic is
27
τn = 5.2383, and the p-value of the test is
p = 1− Φ(τn1,n2) = 1− Φ(5.2383) = 0. (1.35)
Since p is less than 0.01, we reject H0 that mean efficiency of public banks and
foreign banks in India are equal. So, public Indian banks have significantly higher
expected efficiency than foreign banks also. Next, we test for stochastic dominance of
true distribution of efficiency estimates of public banks over empirical distribution of
efficiency estimates of foreign banks operating in India. We reject the null hypothesis
that true distribution function of efficiency estimates of public banks is equal to the
true distribution function of efficiency estimates of foreign banks with a p-value of
0.007195. This implies that the true distribution function of efficiency estimates
of public banks stochastically dominates the true distribution function of efficiency
estimates of foreign banks operating in India.
1.5.3 Discussion
From the analysis above, we can see that our Hypothesis 1 is supported. This
shows that Indian banks have indeed caught up to banks in the U.S. in terms of
efficient banking. Our empirical results provide tentative evidence that diffusion
theory holds in the Indian banking sector, relative to the benchmark study (Sathye
2003). Although we offer some plausible evidence at a strategic level for the diffusion
model, more future research in this direction is warranted. We note that the sample
size of banks in India is much smaller than their U.S. counterparts.
Our Hypothesis 2a and Hypothesis 2b are also supported. These results sup-
port the path dependence argument. The de-regulation policies developed by the
Indian government over the last two decades have not yet had full effect; indeed, do-
28
mestic private and foreign banks lag their public counterparts in terms of operational
efficiency. There appear to be two options for domestic private and foreign banks to
catch up. From a service operations perspective, they should actively seek to attract
the most competitive advantage, creating the requisite knowledge capital. Alterna-
tively, the Indian government may need to do more de-regulation so that the domestic
private and foreign banks can completely match or exceed the public banks, which
is common-place in many market-driven, developed nations. Not only is our finding
explained by path dependence theory (i.e., public banks in India are more efficient
than domestic private and foreign banks due to the advantage that they had for over
40 years until 1990), but also they may have a human capital advantage. Combining
these two hypothesis tests, the KBV of firm is also supported, as attested by the rev-
elations of Indian bank managers, whom we interviewed. These managers reported
that public Indian banks hired “better” employees than domestic private and foreign
banks in India, which may have positively influenced the rates of efficiency diffusion.
1.6 Conclusions and Limitations
We compared the operational efficiency of U.S. and Indian banks and com-
pared the relative efficiencies of public, domestic private and foreign banks operating
in India. We grounded our hypotheses in diffusion theory and path dependence theory
and tested them empirically using the test statistic derived by Kneip et al. (2013b).
The assumption of convexity of the production frontier is tested by using the test
statistic derived by Kneip et al. (2013a). To our knowledge, this is the first paper
to test the assumption of convexity of the production frontier in SOM and banking
literature. All the previous papers that have estimated efficiency of banks operating
in the U.S. or in India have used DEA estimator without testing for convexity of the
29
production frontier. However, under the alternative hypothesis of non-convex pro-
duction set, DEA estimator is inconsistent. So, we recommend the explicit testing
for convexity of the production frontier in future research that aims to capture effi-
ciency before applying traditional DEA analyses. Our rejection of null hypothesis of
convexity of the production frontier is consistent with the findings of Wheelock and
Wilson (2011) and Wheelock and Wilson (2012) in parametric settings.
Although diffusion theory and path dependence theory have been used exten-
sively in research, this paper is among the first to ground hypotheses in these two
theories in SOM banking sector research and test them empirically. We found a signif-
icant difference between the expected efficiency of banks operating in India and in the
U.S. When compared to the Sathye (2003) benchmark research, our results indicate
that Indian banks may have caught up with U.S. banks in terms of efficient banking
due to the diffusion of technology and best banking practices from the western world
to the emerging market economies. This diffusion may have also been enabled by the
widespread outsourcing of advanced telecommunications and information technology
to Indian firms over the past two decades. Similarly, the finding that state-owned
Indian banks are more efficient than domestic private and foreign banks operating in
India implies that the public banks still have a competitive advantage due in part to
past government policies that imposed restrictions over domestic private and foreign
banks. Moreover, to the extent that the public sector banks have more competitive
employees, the KBV implemented in services, would suggest that these employees
were better able to capture the best practices and technology transferred to India.
There are some limitations in our study. First, the data we used were secondary
data and they come with certain limitations (see Roth et al. (2010) for a detailed
discussion on this). Second, owing to the slow convergence rate of the FDH estimator,
the sample size of subsample of observations used to test Hypothesis 2a and 2b, nκ,
30
was small. However, test of stochastic dominance supports our results from these
hypotheses tests. Future research is warranted in these areas.
In conclusion, this research offers strategic operations insights for furthering
future SOM research beyond banking. Importantly, our empirical results have impli-
cations for practice and policy. To improve the efficiency of domestic private and for-
eign banks, either they can aggressively pursue talent and/or the Indian government
can carry forward their liberalization and de-regulation policies. Thus, managers
of less-efficient banks can achieve higher efficiency by imitating the highly-efficient
banks. Moreover, the Indian Government of India should continue its reform process
to elevate the banking sector overall. Taken together the substantive and method-
ological contributions add to our strategic operations arsenal and offer a bridge for
advancing operations management more broadly.
31
Essay 2.Effect of Readmission Rates on
Marginal Cost in HospitalServices: An Econometric Analysis
Abstract
We investigate the effect of readmission rates on hospital costs and hospitals’ profit
incentives to reduce readmissions. We consider consequences of the new Medicare
policies that impose reimbursement penalties on hospitals with higher than threshold
readmission rates. Using aggregate level data from 169 Arizona hospitals, we estimate
their marginal costs using structural estimation techniques developed in the empirical
Industrial Organization (IO) literature. Contributing to ongoing hospital and gov-
ernment debates, our empirical results demonstrate that marginal hospital costs do
indeed increase significantly with increases in readmission rates. Taking into account
the readmission cost results, we simulate outcomes under counterfactual market struc-
tures that could arise as result of the new penalty system for Medicare reimbursements
to hospitals. Importantly, we find the plan to implement reimbursement penalty for
32
hospitals with above average readmissions can act to induce competition among hos-
pitals to lower average readmission rates.
2.1 Introduction
In this paper, we subject to rigorous empirical scrutiny of the influence of
hospital readmission on marginal hospital costs. In operations management, a read-
mission coincides with the notion of “rework,” which is a manifestation of a quality
failure. As such, we anticipate that readmissions should increase the marginal cost
of healthcare services. Readmissions are subject to both qualitative and quantitative
external costs (e.g., patient welfare, such as lost wages etc., and added costs to payers,
including private and public). Most recently, the Patient Protection and Affordable
Care Act (PPACA) was implemented to penalize hospitals that are deemed to have
higher than threshold patient readmission rates (hereafter “high” readmission rates)
(Stone and Hoffman 2010). Beginning in 2013, hospitals with high readmission rates
will have their total Medicare reimbursements reduced by 1 percent; this penalty will
be increased in phases until 2015, when they will rise to 3 percent (Rau 2011). The
underlying presumption behind the penalty is this: total healthcare expenditures will
fall if readmission rates decrease. Operationally, then, readmissions represent a hos-
pital’s failure to provide adequate care during the patients’ initial stay in the hospital
and a reimbursement penalty will incentivize hospitals to improve quality.
As a backdrop in 1983, Medicare moved from a “fee-for-service” (FFS) system–
hospital provided the payers with itemized bills for each admitted patient (e.g., a night
in a hospital bed, or for hours of surgery)–to a prospective payment system (PPS).
PPS paid hospitals a fixed fee per case that is based on diagnosis groupings rather
than per service item. It sought to eliminate the strong incentives for hospitals to
33
hold patients for more days than were medically required, which in turn, resulted in
shortened average length of patient stays and reduced hospital over-crowding (Phelps
2012). However, PPS had no measured effects on hospital readmission rates, which
were already high in 1983; thereafter, remained significantly unchanged for three
decades. On average, one in five Medicare patients served by hospitals are readmitted
for the same diagnosis within 30 days of discharge; cumulatively, 35 percent are
readmitted within 90 days of their discharge (Jencks et al. 2009). Unexpectedly,
the PPS payment structure may have actually created strong financial incentives for
hospitals to not reduce readmissions, as the Medicare continued to reimburse fully
for readmitted patients. Thus, the PPACA penalty is the latest in a series of hospital
cost control measures for treating Medicare patients.
Figure 2.1 illustrates how the cost of readmissions and penalties can poten-
tially affect hospitals’ financial incentives. Consider two hospitals with an identical
patient: Hospital 1 is not penalized (i.e., the actual readmission rate is less than the
threshold readmission rate), whereas Hospital 2 is subject to penalties (i.e., the actual
readmission rate is more than the threshold readmission rate). In Hospital 1, a pa-
tient receives a treatment during her first admission, which costs the hospital $10, 000
and the Diagnosis Related Group (DRG) is priced at $15, 000. Since this hospital is
not penalized under the new payment scheme, it is paid $15, 000 by Medicare and
earns a profit of $5, 000. If this same patient is discharged and readmitted within 30
days for the same diagnosis, the hospital’s costs can either increase or decrease. If
the readmitted patient’s state of health is worse upon readmission (versus the initial
admission), the cost of treating the readmitted patient will be higher (i.e., $10, 500
in Figure 2.1); and hence, the total profit earned on the readmission will be lower
($4, 500). Alternatively, if the cost to the Hospital 1 of treating a readmitted patient
is lower ($9, 500) as compared to the first admission (e.g., the surgeon and the hospi-
34
tal staff understand the patient diagnosis and situation better after readmission and
require fewer or more, specific tests and/or less coordination than in the first admis-
sion) then the hospital’s total profit will be higher for a readmitted patient than for
a first time admission ($5, 500). Next we examine the payment structure for Hospital
2 in Figure 2.1, which treats an identical patient as in Hospital 1. Because Hospital 2
is being penalized for its high readmissions, its reimbursement for a first time admis-
sion is automatically reduced in contrast to unpenalized Hospital 1 (i.e., $14, 550 vs.
$15, 000, respectively, in Figure 2.1). Similarly, if this same patient is readmitted to
Hospital 2, its payment is still penalized. Thus, Hospital 2 incurs a penalty for both
its first time admissions and readmissions since its actual readmission rate higher
than threshold. In this example, the penalty is 3 percent on revenues.
Figure 2.1: Illustrative Example of Payment Scheme for Penalized and UnpenalizedHospitals
These illustrations suggest two important unresolved research questions: 1)
35
Without a penalty, do hospitals have financial incentives to either reduce or induce
readmissions? 2) How will the PPACA readmission penalty mechanisms affect hospi-
tals and patients? More specifically regarding the latter, will the new PPACA penalty
scheme reduce average readmission rates of hospitals in any market? This paper ex-
amines these questions by empirically investigating the systematic effects of hospital
incentives under two payment structures–prior to and post PPACA. Namely, we first
evaluate the effect of readmissions on hospital’s marginal cost. Next, we assess the
effect of the new penalty system on readmission rate of hospitals. In doing so, we
acknowledge that there may be other marketplace incentives influencing an individual
hospital readmissions, such as the hospital’s perceived reputation and the effect of
bed utilization, but we are not able to explore these here.
Theoretically, we take the operations management stance that hospital read-
missions are arguably analogous to external failures, which means that the defect is
not identified until the product/service affects with the customer externally to the
setting (e.g., Crosby 1979, Juran 1988, Giffi et al. 1990, Fitzsimmons and Fitzsim-
mons 2008). Manufacturing rework has been shown to increases costs (e.g., Savage
and Seshadri 2003, Alukal 2006). Programs like lean, six-sigma, and lean-six-sigma
can be viewed as “interventions” that when implemented will act to improve product
quality and minimize rework and its associated costs (see Linderman et al. 2003, Shah
and Ward 2003, Rao et al. 2004, Alukal 2006; Schroeder et al. 2008, Zu et al. 2010).
Nonetheless, when external failures occur in manufacturing, the company’s remedial
costs more often than not go beyond those of reproducing the original products. In
addition to the intangibles, added direct tangible costs are associated with the logis-
tics and overhead of returning the defective product to its facilities. In contrast, as
depicted in Figure 2.1, a hospital’s marginal cost to treat a readmitted patient can be
either lower or higher than the cost of the original treatment (e.g., patient’s health
36
status is better or worse upon readmission than at their initial admission), and/or the
effort to recapture overhead and intangible costs can be either difficult (e.g., system
congestion, added billing and other services, etc.) or easy (e.g., better staff coordina-
tion and knowledge about patient). On one hand, hospitals could have incentives to
readmit in order to capture the charges for the higher patient costs and fill capacity;
on the other hand, if overhead and other costs are not directly recouped, hospital-
s may be naturally incentivized to reduce readmissions even without a government
penalty.
These countervailing perspectives on incentives create a dilemma regarding the
operational impact on hospital marginal costs. Recognizing the inherent complexity in
assessing hospital costs and the general lack of transparency, it is imperative for both
hospital administrators and payers to have a better understanding of the systematic
effects of patient readmissions (i.e., process failures) on hospital costs–especially, as
the Medicare reimbursement penalty is in play. Despite their importance, little is
known about how these potential process failures actually affect hospital marginal
costs even without penalties, and in turn, patient welfare and the viability of hospital
business models. We operationally define marginal cost as the cost to treat one patient
per episode of stay in the hospital; following the Medicare policy, we define a quality
failure as a readmission within 30 days of discharge.
This research is a first step in this direction by providing broad-based, strate-
gic insights through combinative operations strategy and economics perspectives to
examine quality failures (readmissions) in hospitals. To date, there is no empirical
study that addresses completely our two overarching questions. Friedman and Ba-
su (2004) examined the costs of readmissions but differed in several important ways
from this study. First, we use operations strategy as our theoretical lens to investigate
both quality and cost tradeoffs, while their study was primarily cost focused. Second,
37
Friedman and Basu (2004) computed readmission costs to the payer, whereas we esti-
mate marginal cost incurred by the hospital. This distinction highlights differences in
methodology. To estimate marginal cost, we use structural estimation technique de-
veloped in the empirical Industrial Organization (IO) literature (Berry 1994), which
had the added advantage of allowing us to conduct counterfactual analyses of the
market.
We employ secondary data that capture operational and financial variables
from hospitals in Arizona to develop a demand estimation model involving demand,
price, and other hospital characteristics. We then take our demand estimates and ap-
ply the methods in Berry et al. (1995) to estimate the supply side of the model which
uncovers the effect of readmissions on marginal cost. Finally, we model and simulate
outcomes under counterfactual market structures that could arise from the Medicare
penalty. The first counterfactual examines the effect of the proposed penalty on the
hospitals’ decision to reduce their readmission rates. The second counterfactual re-
moves critical access hospitals–those perceived to be at risk of shutting down because
of cost cutting–from the market–and measures the potential welfare loss of patients
due to the high prices that the other remaining hospitals could charge. Insights from
this study have the potential to inform both operations management in healthcare as
well as provide timely insight about healthcare practices. Further, we provide insight
into the current discussions about key policy decisions, such as funding levels for crit-
ical access hospitals (see, for example, Scott 2012). Finally, the incorporation of the
estimation methods from empirical IO literature also contributes to the operations
management literature by suggesting other methods to analyze secondary data.
The rest of this paper is organized in the following way. We review relevant
literature, present our hypothesis in Section 2.2 and describe our data in Section
2.3. We explain our econometric specification and estimation strategy in Section 2.4.
38
We present results in Section 2.5 and discuss the implications of these results and
conclude in Section 2.6.
2.2 Literature and Hypothesis Development
We broadly review three major streams of literature. First, we present a multi-
disciplinary review of the relevant healthcare literature from operations strategy and
quality management to describe our conceptualization of a readmission as a quality
defect. We consider the nature of quality failures as either internal or external and
describe the salient dimensions of quality. Second, taking a medical and management
perspective, we summarize the issues related to nurse staffing on patient outcomes and
costs. Third, we cover structural estimation procedures drawing upon the economics
and operations management literature.
There are multiple operations management studies about strategic healthcare
delivery decisions (see Roth et al. 1996 for a discussion on hospitals’ operations s-
trategies) as well as analytical articles about capacity requirements (e.g., number of
beds, staffing, etc.) and surgical scheduling and patient flow models (see Green 2004
for a detailed review). The rapidity of change in healthcare delivery systems has
escalated over the past decade. Advances in clinical technologies (e.g., faster MRIs,
improvement in radiology technologies, etc.), changes in management practices (e.g.
lean-six-sigma, computerized medical records, etc.) and incorporation of penalties
in payers’ reimbursement policies all potentially affect hospital costs. Yet, there is
a dearth of operations management literature on readmissions in this dynamic envi-
ronment. KC and Terwieschs (2012) seminal work is an exception. They examined
the probability that an individual patient moved from an intensive care unit (ICU) to
step down care center had to be readmitted back (internally) into the ICU. KC and
39
Terwiesch (2012) found that the probability of readmission to the ICU increased as
the initial length of stay (LOS) of the patient decreased. Our study differs from theirs
in important ways. First, our research provides additional insights by using using the
hospital as the unit of analysis instead of the patient. Aggregating up from the patient
to the hospital level would require the precise assessment of all factors that influence
marginal hospital costs. Arguably, many of these transactions and overhead costs
on individuals can not be easily measured as attributed to readmission status (e.g.,
added staff coordination, external communications to family members, etc.). Second,
from an operations strategy perspective, with a hospital as the unit of analysis, we
capture, in part, the systematic aggregate effects of readmissions on the hospital’s
marginal cost. Third, we examine actual hospital discharge and readmission data
versus using internal patient transfers from the ICU to a step down care unit within
the same hospital. Using operations and quality management terminology, our study
evaluates patient readmissions in terms of external quality failures, whereas KC and
Terwiesch (2012) examined internal quality failures. In summary, these are two com-
plementary but different perspectives that together provide more holistic view of the
operational implications of patient readmissions on patients and costs.
Using operations strategy as a theoretical lens for understanding quality (Garvin
1987), hospital readmission signifies unacceptable quality. Notably, a readmission
does not meet patients’ needs for effective, safe care nor achieve “freedom from defi-
ciencies” (Juran 1992), which is a basic assumption for quality. From this viewpoint,
a hospital with a higher readmission rate relative to its peers is perceived as having
poor quality (Rau 2011). Quality is a multidimensional construct. Garvin (1987) i-
dentified eight dimensions of quality (performance, features, reliability, conformance,
durability, serviceability, aesthetics, and perceived quality) in the manufacturing sec-
tor. While in general, these same dimensions with perhaps the exception of durability,
40
also apply to healthcare service quality.
Performance quality coincides with the depth of treatment, such as the use
of advanced technologies for diagnosis. The feature dimension covers the ancillary
services provided, such as meal choices, pre-admission patient information, or even
the scope of the hospital’s discharge plans. For example, if the plan does not en-
sure that follow-up treatments can continue after the patient is discharged from the
hospital, the readmission rate could be affected. The reliability dimension refers to
a hospital’s ability to provide consistently the correct interventions for every patien-
t. Metaphorically, when a patient “falls through the cracks,” in the care process, it
could conceivably affect readmission probability. The conformance dimension is very
relevant to hospital care quality, since it includes whether the correct treatment was
delivered on time and met medical specifications. In hospitals, all service providers
are expected to follow the specific patient care path requirements; external customer-
s (patients) when capable, are informed of clinical requirements and procedures for
their own care (e.g., walking after surgery, taking medications after discharge); their
own involvement impacts their healing process. Deviations on the part of service
providers and/or patients can have some bearing on readmissions. Likewise, service-
ability, which is the ease of servicing a product after sale or in this context the ability
of a discharged patient to obtain services needed, such as assistance with billing,
and availability and access to needed information. We anticipate that the latter is
particularly relevant to readmissions. For example, when the patient has concerns
about her discharge care plan or how to respond to unexpected health events, can
the patient easily receive the required information? So, low serviceability may lead
to readmission if the discharged patient could not receive services needed to perform
her discharge plan. Aesthetics can affect patient satisfaction with the overall hospital
experience. The extent to which dissatisfaction with the “look and feel” and other
41
intangibles causes mental anguish during the hospital stay, influences the patient’s
outcomes after discharge, and in turn, readmissions could be affected. It would be
difficult to explicitly capture how the dimensions of quality individually act to in-
fluence readmissions; however, we contend that each works in concert with others to
define “quality of patient care” (hereafter quality). While we do not explicitly investi-
gate this link in our study, such deviations from quality could be termed “avoidable”
causes of readmissions, which is an area for future research.
In health care research, staffing studies, especially on nurses, are pervasive. Yet
those that investigate how the number of hours of care by nurses, the level of nurse
staffing and the nurses’ working conditions affect the quality of care outcomes have
had mixed results (see Pronovost et al. 2001 Needleman et al. 2002, Stone et al. 2007,
Penoyer 2010). Moreover, other studies relating staffing to costs are also inconsistent.
Some found positive relationships between nurse staffing level and hospital costs (e.g.,
McCue et al. 2003) and others, negative relationships (see Thungjaroenkul et al. 2007
for a detailed survey of all past findings).
Drawing upon the industrial organization literature in economics, structural
estimation-a procedure that has its theoretical basis rooted in economics literature,
offers a way to assess marginal costs that may be useful in health care, where the
transparency and availability of such data is sparse. In economics, Berry (1994) used
structural estimation technique to model standard demand and supply equations,
wherein he modeled demand as a discrete-choice model and assumed that prices are
endogenously determined by various firms in a market. Berry’s (1994) technique was
used to study various demand models of differentiated product segments and these
kind of models are now well-known as “Demand Estimation Models.” In operations
management, Olivares et al. (2008) used structural estimation technique to analyze
operating room scheduling decisions and found that the scheduling managers purpose-
42
ly try to avoid incurring over-time costs. Recently, Allon et al. (2011) used structural
estimation technique to estimate the the value of reducing customer wait times in the
drive-thru fast-food industry and Deshpande and Arikan (2012) used the technique
to impute the overage to underage cost ratio of the newsvendor model in the airline
industry and found that airlines usually “under-emphasize” flight delays.
Given the above, both operations researchers (e.g., KC and Terwiesch 2012)
and healthcare researchers (Chen et al. 1999, DesHarnais et al. 2000) consider high
rates of hospital readmissions to be indicators of poor quality of care. As indicated
earlier, operations strategy posits that rework increases a companys cost (e.g., Giffi
et al. 1990, Savage and Seshadri 2003, Alukal 2006). Thus, hospital readmissions are
cast as rework that occur because some portions of the care process provided during
the original hospitalization had an adverse impact on patient clinical outcomes 1,
which resulted in the need for the patient to be readmitted. This logic also appears
to underpin the PPACA legislation. Thus, from operations management theory of
quality, the marginal cost of a hospital with high readmission rates should be system-
atically higher than a hospital with lower readmission rates. In essence, a hospital
with high readmission rates could potentially have the medical equivalent of a hidden
factory’s costs (Miller and Vollman 1985), but also have a second stream of revenue.
More formally stated:
H1: Hospitals with high readmission rates will have higher marginal cost, ceteris
paribus
1Note that this notion of defect applies to readmissions that are in some sense ‘avoidable’ and notthose that are ‘unavoidable’ or non-preventable on the part of the hospital. The notions of avoidableand unavoidable readmissions are a current topic of interest in the health care literature but we areunable to separate them in this research.
43
2.3 Data
To test our hypotheses, we combine multiple datasets for all hospitals oper-
ating in the state of Arizona from 2008-2010. The data on hospital characteristics,
including the ownership type, type of hospital, provision of emergency service, and
readmission rates came from the Center for Medicare and Medicaid Services (CMS-
Hospital Compare website). Other data needed to estimate marginal costs, including
average price, demand, and other hospital characteristics (i.e., the number of bed-
s, the length of the patient stay, the nurse staffing level, and provision of trauma
care) was obtained from the Arizona State Department of Health’s website. We use
a unique hospital identifier variable to merge the two datasets. The data for these
variables was gathered for 56 hospitals operating in Arizona in 2008 and 2009, and for
57 hospitals operating in 2010 (of which 56 are the same as those in 2008 and 2009; 1
hospital is different). The descriptive statistics of the key variables are given in Table
2.1. Price is defined as the ratio of gross revenue of a hospital to the total number
of patients. Demand is defined as the total number of patients served by a hospital.
Beds is defined as the total number of staffed beds in a hospital. Average LOS is
computed as the ratio of total length of stay in a hospital to demand. Nurse Staffing
(FTE) is the full time equivalence of registered nurses working in a hospital. Nurse
ratio is computed as the ratio of nurse staffing to demand. Since the data set included
all hospital admissions in these hospitals for the three year period, there was a large
variance in average price, demand, number of beds, average length of patient stay,
nurse staffing level (full-time equivalence), and ratio of nurse staffing level (full-time
equivalence) to total patients admitted.
Data on the number of readmitted patients and case-mix adjusted percent
readmissions of heart attack, heart failure, and pneumonia were obtained from CMS.
and Gawande (2013) published their findings on the relationship between occurrence
of surgical complications and hospital finances. Their empirical findings using data
of a Texas hospital system indicate that hospitals have financial incentives to create
surgical complications since these complications change the diagnosis related group
(DRG) of the surgery, which in turn increases the payment from the Medicare. As
79
indicated above, the effect of readmissions on financial incentives for government and
hospitals was recently examined by Friedman and Basu (2004) and Venkataraman
et al. (2013) respectively. However, the impact of the potential penalization plan,
including the threshold value allowed by the government and the penalty structure
on the optimal readmission rate and patient welfare remains yet to be analyzed. This
paper fills in this literature gap.
Principal-agent model and queueing models have been used often in the health-
care and quality operations management literature. So and Tang (2000) develop a
mathematical model to understand the effect of reimbursement policy for drugs on
the drug usage by the clinic. They find that patients with worse initial conditions
and drugs with lower profit margin will force the clinics to set a lower output target
level of the patients’ well being. They also find that the clinics will set a lower output
target level if the reimbursement threshold set by the payer for a particular drug is
lower, which is intuitive. Fuloria and Zenios (2001) develop a dynamic principal-agent
model to outline the FFS payment system of Medicare (purchaser of medical services)
and a hospital (provider), where the Medicare’s problem is to maximize the social
welfare and hospital’s problem is to maximize its expected profit. They find that the
Medicare should move to a prospective payment system with a retrospective penalty
on deaths occurring in the hospital. Our problem is similar, however, the current
system itself is of prospective payment and we do not consider linear payment system
as considered by them. Jiang et al. (2013) model pay for performance outpatient
healthcare system as a principal-agent model where the payer’s (principal) problem
is to minimize the cost while achieving a target waiting time for the patient and the
hospital’s problem is to maximize its profit given the contracting terms by the princi-
pal. The hospital dynamics are modeled as a M/D/1 queueing system. They find that
the linear contract cannot achieve the second-best solution and propose a threshold
80
penalty payment system. Chao et al. (2003) analyze customer flows between different
sites in a multisite healthcare system and provide guidelines for resource allocation
in such cases while meeting a target for waiting time of patients. Anand et al. (2011)
study customer-intensive queueing systems where quality and speed are trade-offs.
They find that customer intensity leads to results different from those of conventional
queueing systems. In particular, the speed of the servers reduces as the number of
competing servers goes up and the price charged by the server increases as the number
of competing servers goes up. We build on this stream of literature by modeling a
prospective payment system healthcare service as a principal-agent model with gov-
ernment (payer) being the principal hospital (provider) being the agent. The payer’s
problem is to maximize its expected profit, which is modeled as a weighted average
of hospital’s expected profit, patient welfare and payer’s cost, which is explained in
detail in Section 3.3.
3.3 Model
Timeline of events of admission and readmission to a hospital and the payment
details are shown in Figure 3.2 and all the notations used in the model are listed in
Table 3.1.
We assume k ∼ BIN(N, r) and since N is sufficiently large, we use normal approxima-
tion to binomial. So, k ∼ N(Nr,Nr(1− r)), and X =k −Nr√Nr(1− r)
∼ N(0, 1). The
hospital gets full payment (pN) from Medicare if its realized readmission rate (k/N)
is lower than the threshold readmission rate (α) while it gets a penalized payment
(pδN) if its realized readmission rate (k/N) is greater than the threshold readmission
rate (α).
81
Figure 3.2: Timeline
Expected Revenue = Pr
[k
N≤ α
](Exp. Rev. | k
N≤ α
)+ Pr
[k
N> α
](Exp. Rev. | k
N> α
)= Pr
[k
N≤ α
](pN + pk | k
N≤ α
)+ Pr
[k
N> α
](δpN + δpk | k
N> α
).
E[k; k ≤ Nα] = E[√Nr(1− r)X +Nr;
√Nr(1− r)X +Nr ≤ Nα]
=√Nr(1− r)E
[X;X ≤ N(α− r)√
Nr(1− r)
]
+NrE
[1;X ≤ N(α− r)√
Nr(1− r)
]
= −√Nr(1− r)
2πexp
−N
2(α− r)2
2Nr(1− r)
+NrΦ
(N(α− r)√Nr(1− r)
).
82
Table 3.1: Notation Table
Notation DescriptionN Number of admitted patients per yeark Number of readmitted patients per year (Random Variable)α Threshold readmission ratep Price per patientr Probability of readmissionδ Payment factor for penalized hospitalsc Cost of treating a patientw Wait time cost per patient
E[k; k > Nα] = E[√Nr(1− r)X +Nr;
√Nr(1− r)X +Nr > Nα]
=√Nr(1− r)E
[X;X >
N(α− r)√Nr(1− r)
]
+NrE
[1;X >
N(α− r)√Nr(1− r)
]
=
√Nr(1− r)
2πexp
−N
2(α− r)2
2Nr(1− r)
+Nr
[1− Φ
(N(α− r)√Nr(1− r)
)].
So, Expected Revenue = pNΦ
(N(α− r)√Nr(1− r)
)(1 + r)(1− δ) + pδN(1 + r)
+ p(δ − 1)
√Nr(1− r)
2πexp
−N
2(α− r)2
2Nr(1− r)
.
The admission and readmission process is modeled as a queueing network with
feedback as shown in Figure 3.3. Further, we use queueing theory results (Kulkarni
2005) to model the hospital cost and patient wait time cost for patient welfare, that
we use later in government’s objective function.
83
Figure 3.3: Queueing with Feedback
Time Spent by a patient in a hospital =1
(1− r)µ−N
Hospital Cost =cN
(1− r)µ−N, (3.59)
where µ is the hospital capacity. Similarly,
Patient Cost =wN
(1− r)µ−N. (3.60)
So, the hospital’s expected profit is given by the difference between its expected
revenue and cost.
Hospital Profit = pNΦ
(N(α− r)√Nr(1− r)
)(1 + r)(1− δ) + pδN(1 + r)
+ p(δ − 1)
√Nr(1− r)
2πexp
−N
2(α− r)2
2Nr(1− r)
− cN
(1− r)µ−N.
(3.61)
84
The government side problem is modeled as optimizing the weighted average
of hospital’s profit, patient welfare, and government’s cost (which is equal to the
hospital’s revenue). Using Equations 3.59 and 3.60, government’s objective is given
Code to produce Figure 3.5 is similar to the above and hence is omitted for brevity.
129
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